A class of modified high‐order autoregressive models with improved resolution of low‐frequency cycles

Alex S. Morton and Granville Tunnicliffe‐Wilson

Journal of Time Series Analysis, 2004, vol. 25, issue 2, 235-250

Abstract: Abstract. We consider regularly sampled processes that have most of their spectral power at low frequencies. A simple example of such a process is used to demonstrate that the standard autoregressive (AR) model, with its order selected by an information criterion, can provide a poor approximation to the process. In particular, it can result in poor multi‐step predictions. We propose instead the use of a class of pth order AR models obtained by the addition of a pre‐specified pth order moving average term. We present a re‐parameterization of this model and show that with a low order it can provide a very good approximation to the process and its multi‐step predictions. Methods of model identification and estimation are presented, based on a transformed sample spectrum, and modified partial autocorrelations. The method is also illustrated on a real example.

Date: 2004
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